Abstract

In toroidal geometry, and prior to the establishment of a fully developed turbulent state, the so-called topological instability of the pressure-gradient-driven turbulence is observed. In this intermediate state, a narrow spectral band of modes dominates the dynamics, giving rise to the formation of isosurfaces of electric potential with a complicated topology. Since advection of tracer particles takes place along these isosurfaces, their topological complexity affects the characteristic features of radial and poloidal transport dramatically. In particular, they both become strongly nondiffusive and non-Gaussian. Since radial transport determines the system confinement properties and poloidal transport controls the equilibration dynamics (on any magnetic surface), the development of nondiffusive models in both directions is thus of physical interest. In previous work, a fractional model to describe radial transport was constructed by the authors. In this contribution, recent results on periodic fractional models are exploited for the construction of an effective model of poloidal transport. Numerical computations using a three-dimensional reduced magnetohydrodynamic set of equations are compared with analytical solutions of the fractional periodic model. It is shown that the aforementioned analytical solutions accurately describe poloidal transport, which turns out to be superdiffusive with index .

Received 15 November 2007Accepted 04 March 2008Published online 10 April 2008

Acknowledgments:

This research was sponsored by the DGICYT (Dirección General de Investigaciones Científicas y Tecnológicas) of Spain under Project Nos. ENE2004-04319 and ENE2006-15244-C03-01 and by CM-UC3M (Comunidad de Madrid—Universidad Carlos III) Project No. CCG06-UC3M/ESP-0815. Part of this research was sponsored by the Laboratory Research and Development Program of Oak Ridge National Laboratory, managed by UT-Battelle, LLC, for the U.S. Department of Energy under Contract No. DE-AC05-00OR22725. L.G. acknowledges the financial support of Secretaría de Estado de Universidades e Investigación of Spain during his stay at Oak Ridge National Laboratory.